In principle, writing a funding proposal is supposed to give you an opportunity to reflect on your research program, think about different directions, and get new insights about projects not yet started. In practice it is a time of copious writing and anxiety, coupled with a lack of sleep! However, I have to admit that today my experience was the former: I figured out (in preparing my Exoplanet Research Program proposal for NASA) that I have been missing some very low-hanging fruit in my thinking about the the error budget for extreme precision radial-velocity experiments:
RVs are obtained (usually) by cross-correlations, and cross-correlations only come close to saturating the Cramér–Rao bound when the template spectrum is extremely similar to the true spectrum. That just isn't even close to true for most pipelines. Could this be a big term in the error budget? Maybe not, but it has the great property that I can compute it. That's unlike most of the other terms in the error budget! I had a call with Megan Bedell (Chicago) at the end of the day to discuss the details of this. (This also relates to things I am doing with Jason Cao (NYU).)
In other news, I spent time reading about linear algebra, (oddly) to brush up on some notational things I have been kicking around. I read about tensors in Kusse and Westwig and, in the end, I was a bit disappointed: They never use the transpose operator on vectors, which I think is a mistake. However, I did finally (duh) understand the difference between contravariant and covariant tensor components, and why I have been able to do non-orthonormal geometry (my loyal reader knows that I think of statistics as a sub-field of geometry) for years without ever worrying about this issue.
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